Question

question 1 of 10, step 1 of 3
solve the system of two linear inequalities graphically.
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$$\begin{cases} y \\leq -5x + 10 \\\\ y > x - 2 \\end{cases}$$

step 1 of 3: graph the solution set of the first linear inequality.

Explanation:

Step1: Identify boundary line

The boundary of $y \leq -5x + 10$ is the line $y = -5x + 10$.

Step2: Find intercepts for plotting

• x-intercept: Set $y=0$, solve $0 = -5x + 10$ → $5x=10$ → $x=2$. So intercept is $(2, 0)$.
• y-intercept: Set $x=0$, solve $y = -5(0) + 10$ → $y=10$. So intercept is $(0, 10)$.

Step3: Draw boundary line

Since the inequality is $\leq$, draw a solid line connecting $(2, 0)$ and $(0, 10)$.

Step4: Shade the solution region

Test the origin $(0,0)$: $0 \leq -5(0)+10$ → $0 \leq 10$, which is true. Shade the region below (and including) the solid line.

Answer:

1. Draw a solid line through points $(2, 0)$ and $(0, 10)$ (the boundary $y=-5x+10$).
2. Shade the region that lies below this solid line (including the line itself) to represent the solution set of $y \leq -5x + 10$.